Digital-to-analog converters (DACs) are widely used in various fields. Among different types of DACs, a sigma-delta, or noise shaped DAC is applied to widespread use. To reduce the required number of analog elements used in the DAC, a plurality of sub-DACs are used rather than a signal DAC with 2N levels. That is, a segmented DAC is used. The DAC converts N binary-weighted bits into M equally-weighted bits, where M=2N.
FIG. 1 is a block diagram schematically showing a prior art segmented DAC 10. As shown, an input word Xin of 20 bits is quantized by a digital modulator 12 into a low-bit word Xm. In this example, the digital modulator 10 is implemented by a 6-bit sigma-delta modulator, so that the input word Xin is modulated into a 6-bit word Xm. The 6-bit word Xm is split into three most significant bits (MSBs) and three least significant bits (LSBs). The three LSBs are converted into eight equally-weighted bits by a thermometer encoder 21 and randomly scrambled by a scrambler 25. The three MSBs are converted into eight equally-weighted bits by a thermometer encoder 31 and the equally-weighted bits are randomly scrambled into scrambled bits by a scrambler 35. Since one MSB bit is equivalent to 8 times of one LSB bit, the MSBs and LSBs are respectively converted by a DAC 29 (8×) and a DAC 39 (1×). That is, a bit weight ratio of the outputs of the DAC 29 and DAC 39 is 8:1. Then the outputs of the DAC 29 and the DAC 39 are summed by a summing unit 40. Ideally, the output of the summing unit 40 should be an analog value that equals to the 6-bit digital word Xm.
However, since the outputs of the DAC 29 and DAC 39 are summed in an analog manner, errors resulting from gain mismatch between the DAC 29 and the DAC 39 cause in-band noise and distortion. Therefore, an in-band signal-to-noise ratio (SNR) and total-harmonic-distortion (THD) of the DAC will be degraded.